How To Analyze FSS-Based EBG Surfaces?(Part I)

1. How To Analyze FSS-Based EBG Surfaces?(Part I) B96901128 王郁翔

2. Review • Space-filling curve high impedance surfaces. • Microminiaturization (0.25->0.076 λ) in 2.4GHz to 2.55GHz • Directivity(8.5->15dBi)and efficiency (9->22%)in 1.58GHz to 1.62GHz • In resonance frequency, |S11| become 1/10 while loss tangent is 0.1.

3. Review • Can we do better? • Why we use space-filling curve? • How to design? • We have to know how to analyze before we design. That’s today’s topic!! • Ex: equivalent circuit model

4. The traditional analysis way is insufficient at high frequency. So we need a more rigorous method to derive equivalent networks for designing reflection and dispersion properties. The innovative part will be covered in Part II. In Part I, we emphasize on basic knowledge.

5. Outline for Part I • Introduction • Design and Analysis Concepts • Quasi-Static Admittance Models • Traditional MoM Analysis • Conclusion for Part I • Reference

6. Introduction • What is FSS-based EBG surfaces? • An EBG structures fabricated by FSS printed on grounded stratified dielectric media. • Why use FSS? • It’s easy to fabricate thus it’s cheaper.

7. What Can It Do? • PEC/PMC/Hard/Soft [1] Stefano Maci, Per-Simon Kildal, “Hard and soft surfaces realized by FSS printed on grounded dielectric slab,” 2004.

8. What Can It Do? • Suppression of surface wave coupling(Ch 11) • Improve planar antenna efficiency • Compact antenna • Resonators[2] • Suppression of parallel-plate waveguide modes[3]

9. Design and Analysis Concepts • Two important parameters to design: reflection properties and dispersion properties.

10. Design Reflection • The angle of reflection coefficient versus frequency. • As flat as possible around zero-degree. • Invariant with respect to the incidence angle and for both TE and TM.

11. Design Dispersion • Enlarge the SW frequency stop band. • Reduce the dependence on the SW direction of propagation along the surface. • Change the shape and stratification of the printed elements to change reflection and dispersion properties.

12. Quasi-Static Admittance Models • Use LC equivalent circuit. These parameters are derived by dominant Floquet mode. • Patch-type FSS &Aperture-type FSS

13. Quasi-Static Admittance Models • In low frequency, patch-type exhibits a capacitive behavior and aperture-type exhibits an inductive behavior. • Use horizontal transmission line to replace vertical transmission line to connect periodic cells.

14. Quasi-Static Admittance Models • However, for high frequencies, the LC parameters are dependent on the phasing and polarization. • Quasi-static admittance models doesn’t work at high frequency.

15. Method of Moments • Apply when boundary condition extend to infinity.(FDTD doesn’t work) • Discretize integral equation and use linear algebra to solve the problem. • Ex: Given potential, find the charge distribution.

16. MoM for Patch-Type FSS • Boundary condition: • Use spectral MoM and change it into: • We want to find I. • What is V and Z ??

17. MoM for Patch-Type FSS • From equivalence theorem, patches radiating with the Green’s function. • Expressed equivalent currents in terms of subdomain triangular basis functions[4].

18. MoM for Patch-Type FSS • Apply Floquet theorem, the analysis is reduced to a single periodic cell.

19. MoM for Patch-Type FSS • We can express V and Z: • M: numbers of FW modes • m,n from 1 to N, numbers of basis functions

20. MoM for Patch-Type FSS • The Green’s function impedance is the same as transmission line. • Finally, we can express MoM impedance: • Green’s function impedance is a diagonal matrix.

21. MoM for Aperture-Type FSS • Use magnetic current approach instead.

22. MoM for Dispersion Equation • Nontrivial solutions for zero impressed field. • We can change it into: • EBG when no real propagating (kx,ky) solutions exist for a given w.

23. Conclusions for Part I • We’ve learned the basic knowledge about EBG now. • We’ve learned the traditional analysis ways. • We’ll develop more rigorous methods in Part II.

24. Next Time • Define a two-port admittance matrix corresponding to the dominant TE/TM FW of the exact Floquet expansion. • Characterized it by the poles and zeros of its eigenvalues. • Closed-form approximation of dispersion equation. • Reconstruct dispersion diagram from few points to save computation time.

25. Reference • [1] Stefano Maci, Per-Simon Kildal, “Hard and soft surfaces realized by FSS printed on grounded dielectric slab,” 2004. • [2] M. Caiazzo, S. Maci, and N. Engheta, “A metamaterial slab for compact cavity resonators,” IEEE Antennas Wireless Propag. Lett., vol. 3, pp. 261–264, 2004. • [3] Y. Zhang, J. von Hagen, M. Younis, C. Fischer, and W. Wiesbeck, “Planar artificial magnetic conductors and patch antennas,” IEEE Trans. Antennas Propag., Special Issue on Metamaterials, vol. 51, pp. 2704–2712, Oct. 2003.

26. Reference • [4] R. Orto and R. Tascone, “Planar periodic structures,” in Frequency Selective Surfaces,(J. C. Vardaxoglou Ed.), Research Studies Press, Taunton, England, 1997, Chapter 7, pp. 221–275. • [5] Textbook Ch11,13,14